Answer
The solution set is $\left\{-\frac{9}{8}, \frac{9}{8}\right\}$.
Work Step by Step
Add $-81$ to both sides to find:
$64x^2-81=0
\\(8x)^2-9^2=0$
RECALL:
A difference of two squares can be factored using the formula:
$a^2-b^2=(a-b)(a+b)$
Factor the difference of two squares to find:
$(8x-9)(8x+9)=0$
Equate each factor to 0 then solve each equation to find:
$8x-9=0 \text{ or } 8x+9=0\\
8x=9 \text{ or } 8x=-9
\\x=\frac{9}{8} \text{ or } x=-\frac{9}{8}$
The solution set is $\left\{-\frac{9}{8}, \frac{9}{8}\right\}$.
